Spherical coordinate target position computer



M. D. SHQLTZ 3,197,294

SPHERICAL cooammxm TARGET posmou COMPUTER Gct. 15, 1963 Filed Ma.y 27, 1960 INVENTQR. MITCHELL D. SHOLTZ Oct. 15, 1963 M. is. SHOLTZ 3107294 SPHERICAL coom mms TARGET posmon COMPUTER Filed May 27. 1960 2 SheetsSheet 2 L06 s//v 6 vou4as DEGREES LAT/7'UDE INVENTO R. MITCHELL D. SHOLTZ 3,107,294 SPHERICAL COORDINATE TARGET PSITION COMPUTER Mitcheii D. Sholtz, Phoenixville, Pa., assignor to the United States of America as represented by the Secretary of the Navy Filed May 27, 1960, Ser. No. 32,494 3 Claims. (Cl. 235187) (Granted under Title 35, U.S. Code (1952), sec, 266) The invention herein described may be manufactured and used by or for. the Government ofthe United States of America for governniental purpcses Without the payment of any royalties thereon or therefor.

This invention relates to dead reckoningcomputers, and more particularly relates to a computer :Eor computing the longitude-latitude of an object.

This invention is directed to the soiution of a deed reckoning prohlem involving the determination of the longitude-latitude position of a target r object where the targets hearing and range from a marker is known and the longitude-lrtitude position of the marker is known. This invention is especially suitable for use in an aircraft equipped with a longitude-latitude position computer and recorder and a radar unit for providing target range and bearing informa-tioh.

An object of this invention, therefore, is the provision of a nove1 computer which will solve the problem re ferred to herenabove.

Another object of the invention is the provision of a nove1 electrical computer having a minimum of moving parts.

A still =further object of the invention is the provision of a novel computer which will provide inormation indicating the longitude-atitude position of the target, referred to hereinabove, without necessity for any further computation.

Yet another object of the invention is the provision of a nove1 computer, as set forth in the precedng paragraphs, which computer Wi1l continuously compute the in5tantaneous longitude-iatitude position of the target.

A nother object of this invention is the provision of a nove1 computer, as set iorth hereinabove, capable of simultaneously and continuously solv-ing Equation 1, sin ;S=s n 6 cos c+co s 19 sin c 005 A; Equation 2, sin C=sin A sin c sin 4 and Equation 3, A aircraft longitude=AE -W/6O miles sec (9; where i; is the unlgnown latitude of the target; 0 is the aircrafts own latitude, c is the range from the aircra t to the target in nautical miles divided by SXY minutes Which re'sults in the range being giyen in terms of degrees great circle are, A is the bearing angle of the target relatiye to the aireraft referenced to a stabilized or true North, C is the iongitude difference between the target andaircraft, AA/ C longitude is the change in the airrafts iongitude from a known marker or point, and is the change in Bast-West nautical miles divided by sixty minutes of are so as to provide the term in degrees of arc from the earths equator.

A still further object of the invention is the provision of a nevel electrical computer, a s set forth in the preceding paragraph, consisting of r elativ ely simple electrica l comporients such as resistors, diodes, saturable core reactors or summing arnplifiers, and the lke.

'The invention rfurther residesin certainnovel features of construction, combinations and arrangements of parts, and further objects and advantages of the invention wii1 3,17,Z94 Patented 30ict. 15,1963

be apparent t0 these skilled in the art to Whi=ch it perta-ins from the iollowing desoription of the preferred embodiment ther eof desc ribd With reference to the accompanying drawings, whichform a part of the specification, and wherein the same eference characters represent corresponding parts throughout the several vieWs, and in whch:

FIG. 1 is a schematic diagram illustrating a spherical navigation problem;

FIG. 2 is a schematic electromechanical diagram of a spher-ical coordi1iate target position computer embodying the invention;

FIG. 3 is ari electri;cal circuit portraying a shaping net- Work;and

FIG. 4 is a graphical representation of a curve of log sin 0 voltage -vs. degrees latitude 0, used to select a voltage ualue proportional to a trigonometric funetion of an angle.

It is to :be understood that the invention is not limited to the details of constructin and arrangement of parts shown in the drawirigs and hereinafittrdescribed in detai1 but is capabie of being otherwise emb odied and of being practiced or carried out in various ways. It is to be further understood that the phraseology or -trmirioiogy employed herein is for the ptrrpose of description and there is no intention -to herein limit the invention beyond the requiremeints of the prior art.

This inven tion comprises a spherical coordinate target position analog computer, FIG. 2, -for contiriuously providing the longitude-latitude positiori T, FIG. 1, of a. target or other object trom an aicraft A/ C having a known longitude and latitude 0,. The longitude andlatitude of the air craft can be provided by conventiral apparatus. Also, conventional radar apparatus is preferably used to measure the range and hearing A frm the aircraft to the target. The range p is prdvided in nautical mi1es divided' by sixty rnintes of 3116 m}vhich represents degrees of great cirdle arc and is refrrd toas range c hereinafter. The hearing A is the bearirig angle otf the target relative .to the aircraft from a staQb-ilized North, which is preferablytrue North since magnetic deviation varie s from =p oint to point on earth.

Thediierence in -lon g l l de between the target and the aircraft is designated asC, FIG 1, and qb is the unlrown lat-i-tude of the target.

Referring to F I G. 2, the computer embodying the invention simultaneously and continuousiy solves the following th1ee equations:

(1) sin =sin 6 cos c-l-cos 0 sin c cos A (2) sin C=sinA sincsinqb and (3) AA/ C iongi tude= A(E-W) miles sec 6/ 60 where:

q;=target latitude t9= aircraft latitude c=p/ 60 degrees greatcircle arc A=target hearing angle reiative .to aircraft rmeasured trom stabilized North C=longitude diterence trom aircraft to target AA/C loggitude=lougitude dfierence from aircraft to aknownpoint A(E-W) miles/6= change in Bast-West nautical miles divided by minutes of arc to give deg rees of arc referencedtothe equator Referring to FIG. 2, an electrical voltage signal proportional to the target latitude qh is obtained in the following marmer.

The computer, FIG. 2, has a potentiorneter unit 10 for permitting an electrical voltage signal to be inserted therein proportional to the latitude of a known point that the aircraft A/ C is currently over. It is preferable that the unit 10 be -adjusted -before the ai.rcraft takes off trom its base which usually has a known latitude. This signal is fed via a line 11 to a saturable reactor 12, which provides a voltage output propor-tional to the instantaneous aircraft latitude in a line 13., When the aircraft flies over the known point or base, cl=osure of a switch 14 in a line 15 permits the feeding of a voltage therethrogh to the saturable reactor 12 from a conventional navigation computer unit 16. The unit 16 provides a signal proportional to change in latitude 0 of the aircraf-t. This signal is easily provided since sixty nautical miles in the North-South direction is equivalent to one degree of latitude change. The saturable reactor 12 functins as a sum-ming arnplifier and accordingly, the sumof the signals from the units 10 and 16 are fed to line 13.

The instantaneous value of the aircrafts latitude 0 is fed via line 13 into a log sin shaping network unit 17, which provides a voltage signal output in a line 18 proportional to log sin 0. The log sin 6 signal is. fed to the input of a saturable reactor 20via the line 18.

When a target is picked up, preferably by a radar unit 21, a voltage signal c proportional to the target range from the aircraft is supplied by the radar unit 21 propor-. tiorial to diflerence in degrees of great cirole arc between the target and the aircraft. This signal 0 is fed via a line 22 to a log cos shaping network unit 23 having a voltage signal output proportional to log cos c in a line 24. The line 24 conducts this signal to the input side of the reactor 20. The output signal of the reactor 20 is a voltage proportional to the sum of the log sin 0 signal and the log, cos c signal, which sum is fed via a line 25, an antilog shaping network unit 26, and a line 27 into a saturable reactor 28. The unit 26 has an output signal voltage proportional to sin 0 cos c which is one of the terms of the trigonometric Equation 1.

If the value of the term sin c cos 0 cos A be zero, which 4 The voltage signal C in line 53 is supplied from a sat rable reactor 54 via a line 55, an anti-log shaping network unit 56, a line 57, and an arc sin shaping network unit r'espectively. The output of the reactor 54 surns three input voltage signals proportional to log sin A, log

sin 0 and log sec 0 conducted via lines 60, 61 and 62, re-

willoccur when angle A is ninety degrees and the target is due East or due West of the aircraft. The signal output of the reactor 28 then will be a voltage proportional to sin 6. The sin ;t signal is fed via a line -30 into an arc sin shaping network unit 3l having a signal voltage output The log sin A signal is provided in the line by a log sin shaping network unit 63 having a voltage signal input proportional to the instantaneous value of A via a branch line 64 of the line 46 leading from the radar unit 21.

The log sin c signalis provided in the line 61 by a log sin shaping network unit 65 having a voltage signal input proportional to the instantaneous value of 0 via a brancl1 line 66 of lines 22 and 44 leading from the radar unit 21.

The log sec j voltage signal in the line 62 is provided by a log sec shaping network unit 67 having an input voltage signal proportonal to picked oi from the line 32 and conducted to the unit 67 via a line 68.

The voltage signal proportional to the instantaneous aircraft longitude position is provided inthe line 52 by means of a saturable reactor 70. The reactor 70 sums input signals proportional to the longitude taken from a known point and the computed change of longitude of the aircraft from the known point via lines 71 and 72, respectively. The voltage signal in the line 71 is provided by adjusting a wiper on a potentiorneter in a unit 73 while the aircraft is at or over the point of known longitude.

Equation 3 is solved by simultaneously supplying a voltage signal 6 to a log sec shaping network 74 via a branch line 75 from the line 13 and feedng log sec 6 a signal via a line 76 to a saturablereactr 77.

The reactor77 sums the log sec 0 signal with a log A(E-W) /60 miles supplied thereto via a line 78 from a log shaping network unit 80. The unit 80 has an input signal fed thereto via a line 81 from the navigation computer 16. The signal in the line 81 is proportional to the degrees of arc traveled by the aircraft in an Bast-West direction referenced to theearths equator.

The output of the reactor 77 is fed to the reactor 70 via a line 82, an anti-log shaping network unit 83 and the line 72.

Each of the shaping network units is conprised of a network of resistances and diodes combined in an e'lec trical circuit, FIG. 3, in.such a marmer that for a given input voltage signal the desired outputvoltage signal is obtairied, FIG. 4 For example, the log sin shaping netproportional to the instantaneous latitude q5 position of the target ina line 32. ]If desired, this signal can be usedto drive a readout counter and/or otherwise suitably applied;

It is understood that although saturable reactors are preferably 'used in this computer, conventional surrm1ing amplifiers may be substituted therefor.

A voltage signal proportional t the term sin c cos 6 cos A is fed into the reactor 28 via a line 33 from an antilog shaping network unit 34. A voltage signal proportional to log sin c+ log cos 0+ log cos A is fed via a line 35 from a saturable reactor 36. The reactor 36 has three voltage signal inputs via lines 37, 38, 39, respectively proportional to log sin c, log cos 0, and log cos A from a log sin shaping network unit 41 and log cos shaping network unit 17 is comprised of a main line resistor and a plurality of diodes 91, 92, 93, 94 electrically connected 'ir1 parallel. Each of the diodes 91, 92, 93, 94 is pieten ably a Zener diode si.uce they aremade available with work units 42 and 43. The unit 41 has a signal input c viaa branch line 44 of the line 22. The unit 42 has a signal input 49 via a branch line 45 of line 13. The unit 43 has a voltage. signal input proportional to the hearing angle A, FIG. 1, via a line 46 from the radar unit 21.

The longitudepositin of the target T, FIG.11, is provided in the form of a voltage signal proportional theret in an output line 50, FIG. 2, from a saturable reactor 51 52 and 53 respe ctively.

of the computer that adds an instantaneos longitude voltage signal and the computed longitude diirerence between known breakdown ratings ranging from 0.3 to 300 volts. Additionally, resistors such as variable resistors 95, 96, 97, 98 are respectively coupled in series with and pre ceding the diodes 91, 92,: 93, 94 so that thebreakdown current can be closely regulated for the purpose of pro viding a curve 101,- FIG. 4, where a voltage signal 6 pro- Portional to degrees latitude of theaircraft is shapeci to be proportionalto log sin 0. More particularly, when the diode 91.;breaks down and conducts, point 10111 can be plotted, when the diodes 91 and 92 are conducting, point 101b is plotted. Similarly, point l0lcis plotted whendiodes 91, 92, 93 are conducting. Point 101d is plotted when the diodes 91, 92, 93, Marc coriducting.

It is understood that asmany resistances and diodes can be used as are desiredor requred; It is theintention tol1ereby cover not only the abov n1entioned modificaton of the preferred construction, but it is the intention tocover all adaptations, modifications, and uses thereof which conie within the practice of these skilledin the art to which the invention relates,and the scope of the appended claims.

What is claimed is:

1. An analog computer for providing voltage signals in an arcraf t prepertienal te the lengtude and latitude of a target, cemprisng; means fer generatng a sgnal propertenal te the lattude of the arcnaft, means fer generatng a signal c prepertenal te the range of the target relatve te the aircraft in terms of degrees of great circle are, means or generatng a sgnal A prepertienal to the bearng angle of thetarget IOII1 the arcraft frem a stabilized Nerth, sgnal shaping netwerk means cennected te said signal 0 generatng means fer providing a signal prepertienal te the leg sin ef said sgnal 6, sgnal shapng netwerk means cennected te said sgnal c generatng means providing a signal prepertenal te the leg cos of said signal c, first sunnnng means electrcally cennected te said leg sin and said leg ces shaping netwerk means fer sumrning said leg sin (9 signal and said leg ces c signal, first anti-leg sgnal shapng netwerk means cennected te said first summng means fer providing a signal prepentenal te sin 0 cos c, signal shapng netwerk means electrically cennected te said sgnal c generatng means fer providing a signal prepertienal te the leg sin of said signal c, signal shapng netwerk means electrically cennected te said signal 0 generatng means fer providing a signal prepertienal to the leg cos of said sgnal 0, shaping netwerk means cenneeted te said sgnal A generatng means fer providing a signal prepertienal te the leg cos of said sgnal A, secend summng means cennected te said leg sin c and said 1eg ees 0 and said leg cos A shapng netwerk means fer summing said leg sin c and said leg ces 0 and said leg cos A signals, secend anti-log signal shaping netwerk means cennected te said secend sunnnng means, thrd summing means cennected te said first and secend anti-leg shaping netwerk means fer providing a sgnal prepertienal te sin i, first arc sin sgnal shapng netwerk means cennected te said third summing means fer providing a signal preportenal te the latitude of the target, signal shaping netwerk means cennected te said sgnal A generatng means fe=r providing a signal prepertenal te the leg sin of said signa-l A, signal shaping netwerk means cennectedte said sgnal c generatng means fer providing a signal prepertienal to the leg sin of said signal c, sgnal shapng netwerk means cennected te said first arc sin signal shaping netwerk means er providing a signal prepertienal te the leg sec of said signal q5, feurth surnmng means cennected te said leg sin A and said leg sin 0 and said leg sec q5 signal shaping netwerk means, thrd antileg signal shapng netwerk means cennected te said feurth snrnrning means fer providing a sgnal propertenal te the sin of said signal c, secend arc sin shaping netwerk means cennected te said feurth summing means fer providing a signal C prepertenal te the degrees longltude dterence between the target and the arcraft, signal shaping netwerk means cennected te said signal 0 generatng means fer providing a sigma] prepertenal te the leg sec ef said signal 9, means generatng a signal propertenal te the degrees of arcraft lengitude change A(EW)/ 60 referenced te the earths equater, signal shaping netwerk means cennected te said A(E-W) 60 sgnal generatng means fer providing a sgnal prepertenal te the leg of said sgnal A(E-W)/60, fifth su.rnrnng means cennected te said leg; sec 0 and leg A(E-W)/6O signal shapng netwerk means, feurth anti-leg sgnal shaping netwerk means cennected te said fifth surmnng means er providing a signal prepertenal te the degrees of aircraft lengitude change frem a peint of knewn lengtude, means fer generatng a signal l prepertienal te the longitude of said knewn peint, and sixth surnrnng means cennected te said fenrth anti-leg signal shaping netwerk means and said signal l generatng means fer providing a signal L prepertional te the lengitnde of the aircraft, and seventh surnrnng means cennected te said sixth summing means and said secend arc sin signal shaping netwerk means fer prevding a signal prepertenal te the lengtude of the target.

2. In an analeg computer fer providing a voltage signal in an areraft prepertienal te the latitude of a target,

G means fe'r generatng a sgnal 0 preportienal te the latitude of the arcraft, means fer generatng a sgnal c prepertionalte the range ef the target relative te the arcraft in terms of degrees of graat circle are, means fer generating a signal A prepertional te the hearing angle of the target frem the aircraft frem a stabilized Nerth, sgnal shaping netwerk means cennected te said signal 0 generatng means for providing a signal prepertenal te the log sin of said signal 0, signal shapng netwerk means cennected te said signal c generatng means providing a signal proportenal te the leg cos of said signal c, first snmmng means electrically cennected te said leg sin and leg ces shapng netwerk means fer sumrnng said log sin 0 sgnal and said leg cos c signal, first anti-leg signal shaping netwerk means cennected te said first surnmng means fer providing a sgnal prepertienal te sin 0 cos c, sgnal shapng netwerk means electrcally cennected te said signal c generatng means fer providing a sgnal prepertenal te the leg sin of said sgnal c, shaping netwerk means electrcally cennected te said sgnal 0 generatng means fer providing a signal preportienal te the leg cos of said sgnal 0, shaping netwerk means cennected te said signal A generatng means fer providing a signal prepertenal te the leg cos of said signal A, seeen-d summing means cennected te said leg sin c and said leg cos 0 and said leg cos A shapng netwerk means fer sumrnng said leg sin 0 and said leg cos 0 and said leg cos A signal, secend anti-leg signal shaping netwerk means cennected te said secend summing means, thrd summing means cennected te said first and secend anti-leg shapng netwerk means fer providing a sgnal prepertional te sin 5, and first arc sin sgnal shaping netwerk means cennected te said thrd surnrnng means fer providing a signal prepertenal te the latitude q! of the target.

3. In an analeg computer rfer providing a voltage signal in an arcraft propertional te the lengitude of a target, means fer generatng a sgnal 0 prepertenal te the latitude of the arcraft, means fer generatng a signal c prepertienal te the range of the target relative te the aircraft in terms of degrees of great circle are, means fer generatng a signal A prepertenal te the hearing angle of the target trom the arcraft frem a stabilized Nerth, means generatng -a signal prepertienal te 21 lattude 45 of the target, sgnal shaping netwerk means cennected te said si=gnal A generatng means ter providing a signal proportienal te the leg sin ef said signa=l A, signal shaping netwerk means cennected te said signal c generatng means fer providing a 'sgnal prepertienal te the leg sin of said signal c, signal shaping netwerk means cennected te said signal generatng means er providing a sgnal prepertenal te the leg sec of said signal ;5, first summng means cennected te said leg sin A and said leg sin 0 and said -leg sec q5 signal shaping netwerk means, first anti-leg signal shapng netwerk means cennected te said first sunnnng means er providing a signal prepertenal te the sin of said sgnal c, arc sin shaping netwerk means cennected te said first anti-leg sgnal shaping netwerk means fer providing a signal C prepertienal te the degrees lengitude dierence between the target and the aincraft, signal shaping netwerk means cennected te said sgnal 0 generatng means fer providing a signal prepertienal te the leg sec of said signal 0, means generatng a signal prepertienal te the degrees of arcraft lengitude change A(E-W)/ 60 referenced te the earths equater, signal shaping netwerk means cennected te said signal generatng means -fer providing a sgnal prepertenal te the leg of said A(E-W) 60 sgnal, secend summng means cennected te said leg sec 0 and leg A(E W)/ 60 signal shapng netwerk means fer summing said leg sec 0 signal and said 1eg A(E-W)/ 60 sgnal, secend anti-leg signal shapng netwerk means cennected te said secend summingmeans fer providing a sgnal prepertenal te the degrees of arcraft lengitude change -frem a point of knewn lengtude, means fer generatng a sgnal l propertienal te the lengitude of 8 References Cited in the file of this patent Reference Dta fox Radio Engineers (4th edtion), July 1957 (International Telephone and Telegraph Corp., New York), pages 104546.

Kornet al.: Electronc Analog Computers (2nd edition) (McGraw-Hill, New York), 1956, page 281. 

1. AN ANALOG COMPUTER FOR PROVIDING VOLTAGE SIGNALS IN AN AIRCRAFT PROPORTIONAL TO THE LONGITUDE AND LATITUDE OF A TARGET, COMPRISING; MEANS FOR GENERATING A SIGNAL O PROPORTIONAL TO THE LATITUDE OF THE AIRCRAFT, MEANS FOR GENERATING A SIGNAL C PROPORTIONAL TO THE RANGE OF THE TARGET RELATIVE TO THE AIRCRAFT IN TERMS OF DEGREES OF GREAT CIRCLE ARC, MEANS FOR GENERATING A SIGNAL A PROPORTIONAL TO THE BEARING ANGLE OF THE TARGET FROM THE AIRCRAFT FROM A STABILIZED NORTH, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID SIGNAL O GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG SIN OF SAID SIGNAL O, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID SIGNAL C GENERATING MEANS PROVIDING A SIGNAL PROPORTIONAL TO THE LOG COS OF SAID SIGNAL C, FIRST SUMMING MEANS ELECTRICALLY CONNECTED TO SAID LOG SIN AND SAID LOG COS SHAPING NETWORK MEANS FOR SUMMING SAID LOG SIN O SIGNAL AND SAID LOG COS C SIGNAL, FIRST ANTI-LOG SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID FIRST SUMMING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO SIN O COS C, SIGNAL SHAPING NETWORK MEANS ELECTRICALLY CONNECTED TO SAID SIGNAL C GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG SIN OF SAID SIGNAL C, SIGNAL SHAPING NETWORK MEANS ELECTRICALLY CONNECTED TO SAID SIGNAL O GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG COS OF SAID SIGNAL O, SHAPING NETWORK MEANS CONNECTED TO SAID SIGNAL A GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG COS OF SAID SIGNAL A, SECOND SUMMING MEANS CONNECTED TO SAID LOG SIN C AND SAID LOG COS O AND SAID LOG COS A SHAPING NETWORK MEANS FOR SUMMING SAID LOG SIN C AND SAID LOG COS O AND SAID LOG COS A SIGNALS, SECOND ANTI-LOG SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID SECOND SUMMING MEANS, THIRD SUMMING MEANS CONNECTED TO SAID FIRST AND SECOND ANTI-LOG SHAPING NETWORK MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO SIN 0, FIRST ARC SIN SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID THIRD SUMMING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LATITUDE 0 OF THE TARGET, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID SIGNAL A GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG SIN OF SAID SIGNAL A, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID SIGNAL C GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG SIN OF SAID SIGNAL C, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID FIRST ARC SIN SIGNAL SHAPING NETWORK MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG SEC OF SAID SIGNAL 0, FOURTH SUMMING MEANS CONNECTED TO SAID LOG SIN A AND SAID LOG SIN C AND SAID LOG SEC 0 SIGNAL SHAPING NETWORK MEANS, THIRD ANTILOG SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID FOURTH SUMMING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE SIN OF SAID SIGNAL C, SECOND ARC SIN SHAPING NETWORK MEANS CONNECTED TO SAID FOURTH SUMMING MEANS FOR PROVIDING A SIGNAL C PROPORTIONAL TO THE DEGREES LONGITUDE DIFFERENCE BETWEEN THE TARGET AND THE AIRCRAFT, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID SIGNAL O GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG SEC OF SAID SIGNAL O, MEANS GENERATING A SIGNAL PROPORTIONAL TO THE DEGREES OF AIRCRAFT LONGITUDE CHANGE $(E-W)/60 REFERENCED TO THE EARTH''S EQUATOR, SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID $(E-W)/60 SIGNAL GENERATING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LOG OF SAID $(E-W)/60, FIFTH SUMMING MEANS CONNECTED TO SAID LOG SEC O AND LOG $(E-W)/60 SIGNAL SHAPING NETWORK MEANS, FOURTH ANTI-LOG SIGNAL SHAPING NETWORK MEANS CONNECTED TO SAID FIFTH SUMMING MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE DEGREES OF AIRCRAFT LONGITUDE CHANGE FROM A POINT OF KNOWN LONGITUDE, MEANS FOR GENERATING A SIGNAL L PROPORTIONAL TO THE LONGITUDE OF SAID KNOWN POINT, AND SIXTH SUMMING MEANS CONNECTED TO SAID FOURTH ANTI-LOG SIGNAL SHAPING NETWORK MEANS AND SAID SIGNAL L GENERATING MEANS FOR PROVIDING A SIGNAL L PROPORTIONAL TO THE LONGITUDE OF THE AIRCRAFT, AND SEVENTH SUMMING MEANS CONNECTED TO SAID SIXTH SUMMING MEANS AND SAID SECOND ARC SIN SIGNAL SHAPING NETWORK MEANS FOR PROVIDING A SIGNAL PROPORTIONAL TO THE LONGITUDE OF THE TARGET. 